Question

Из аэростата, поднимающегося вверх со скоростью 10 м/с, выпал предмет. Найти скорость этого предмета при падении его на землю, построить график зависимости скорости от времени.

Answer 1

Ответ 16м|с летел предмет

Answer 2

Problem Analysis

We are given that a object falls from an ascending balloon with a speed of 10 m/s. We need to find the speed of the object when it hits the ground and plot a graph showing the relationship between speed and time.

Solution

To solve this problem, we can use the equations of motion. The equation that relates initial velocity (u), final velocity (v), acceleration (a), and time (t) is:

v = u + at

In this case, the object is falling under the influence of gravity, so the acceleration (a) is equal to the acceleration due to gravity (g), which is approximately 9.8 m/s^2.

Given that the initial velocity (u) is 10 m/s and the acceleration (a) is -9.8 m/s^2 (negative because it is acting in the opposite direction to the initial velocity), we can substitute these values into the equation to find the final velocity (v) when the object hits the ground.

v = 10 + (-9.8)t

To find the time (t) it takes for the object to hit the ground, we need to consider that the object is falling from a certain height. Let's assume the height is h. The equation that relates height (h), initial velocity (u), acceleration (a), and time (t) is:

h = ut + (1/2)at^2

Since the object is falling from rest (u = 0), the equation simplifies to:

h = (1/2)at^2

We can rearrange this equation to solve for time (t):

t = sqrt(2h/a)

Now we have all the information we need to find the final velocity (v) and plot the graph.

Calculation

Let's assume the height (h) from which the object falls is 100 meters. We can substitute this value into the equation to find the time (t):

t = sqrt(2 * 100 / 9.8) ≈ 4.52 seconds

Now we can substitute the time (t) into the equation for final velocity (v):

v = 10 + (-9.8 * 4.52) ≈ -44.4 m/s

The negative sign indicates that the final velocity is in the opposite direction to the initial velocity.

Graph

To plot the graph showing the relationship between speed and time, we can use the equation:

v = 10 + (-9.8t)

We can choose a range of time values, calculate the corresponding velocity values, and plot them on a graph.

Here is an example graph showing the relationship between speed and time:

import matplotlib.pyplot as plt
import numpy as np

# Define the time range
time = np.linspace(0, 5, 100)

# Calculate the velocity at each time point
velocity = 10 - 9.8 * time

# Plot the graph
plt.plot(time, velocity)
plt.xlabel('Time (s)')
plt.ylabel('Velocity (m/s)')
plt.title('Velocity vs. Time')
plt.grid(True)
plt.show()

The graph will show a linear decrease in velocity over time, starting from an initial velocity of 10 m/s and reaching a final velocity of approximately -44.4 m/s when the object hits the ground.

Note: The graph assumes that the object falls from rest at a height of 100 meters. If the height or initial velocity is different, the graph will change accordingly.

I hope this helps! Let me know if you have any further questions.